[math]100(x-3)=1000[/math]

[math]500(x-3)=5000[/math]

[math]0.03(x-3)=0.3[/math]

[math]0.72(x+2)=7.2[/math]

[size=150]Three students each attempted to solve the equation [math]2(x-9)=10[/math], but got different solutions. Here are their methods. Do you agree with any of their methods, and why?[/size][size=150][size=100][br][br]Noah's method:[br][center][math]\begin{align} 2(x-9)&=10 \\ 2(x-9)+9 &= 10+9 & \text{add 9 to each side} \\ 2x &= 19 \\ 2x \div 2 &= 19 \div 2 & \text{divide each side by 2} \\ x &= \frac{19}{2} \\ \end{align}[/math][/center]Elena's method:[br][center][math]\begin{align} 2(x-9) &= 10 \\ 2x-18 &= 10 & \text{apply the distributive property} \\ 2x-18-18 &= 10-18 & \text{subtract 18 from each side} \\ 2x &= \text-8 \\ 2x \div 2 &= \text-8 \div 2 & \text{divide each side by 2} \\ x &= \text-4 \\ \end{align}[/math][/center][br]Andre's method:[br][center][math]\begin{align} 2(x-9) &= 10 \\ 2x-18 &= 10 & \text{apply the distributive property} \\ 2x-18+18 &= 10+18 & \text{add 18 to each side} \\ 2x &= 28 \\ 2x \div 2 &= 28 \div 2 & \text{divide each side by 2} \\ x &= 14 \\ \end{align}[/math][/center][/size][/size]

[size=150]For each equation, try to solve the equation using each method (dividing each side first, or applying the distributive property first). Some equations are easier to solve by one method than the other. When that is the case, stop doing the harder method and write down the reason you stopped.[/size][br][br][math]2 ,\!000(x-0.03)=6 ,\!000[/math]

[math]2(x+1.25)=3.5[/math]

[math]\frac{1}{4}(4+x)=\frac{4}{3}[/math]

[math]-10(x-1.7)=\text{-}3[/math]

[math]5.4=0.3(x+8)[/math]

Andre wants to buy a backpack. The normal price of the backpack is $40. He notices that a store that sells the backpack is having a 30% off sale. What is the sale price of the backpack?

On the first math exam, 16 students received an A grade.  On the second math exam, 12 students received an A grade. What percentage decrease is that?

[math]2(x-3)=14[/math]

[math]\text{-}5(x-1)=40[/math]

[math]12(x+10)=24[/math]

[math]\frac{1}{6}(x+6)=11[/math]

[math]\frac{5}{7}(x-9)=25[/math]

Select [b]all [/b]expressions that represent a correct solution to the equation [math]6(x+4)=20[/math].

[size=150]Lin and Noah are solving the equation [math]7(x+2)=91[/math].[br][br]Lin starts by using the distributive property. Noah starts by dividing each side by 7.[/size][br][br]Show what Lin's full solution methods might look like.

Show what Noah's full solution methods might look like.

What is the same about their methods?

What is different about their methods?